[math] Trigonometry issue

[ayu]

Ok so I was solving a trigonometry problem, and it was going pretty well i thought, until I checked the answers in the back of the book.


The assignment is "Without a calculator define the angles in 0 <= v <= 180 (degrees) which is the solution for..."

And the assignment that I am having issues with is:

cosv = -cos70 (degrees)

Now what I wanted to do is the following:

v = 360 - (360 - 70) = 70 (degrees)

Since cos is negative I thought that you would have to go in the opposite direction of x, so 70 degrees in the wrong direction basically.

360 - 70 = 290 degrees

So, I thought that since the angle is over 180 degrees I have to try with the point that is on the opposite y side, as in the same x value. As in taking 360 - 290, which is 70 degrees. since the first angle is 290 means that x is positive, so I would have to take the opposite where x is also positive (positive side of y). But the answer that the book gives me is 110, and not 70, which means that x is negative since sin^-1(1) < 110.

So what the book wants me to do is to change the formula to:

v = 180 - 70 = 110 (degrees)

So basically, my question is:

-cos70 != cos-70 ??

And, what does -cos70 mean then?

I can imagine that it mean I simply invert the degrees to the left side, as in if x is positive (70 degrees) then I should just take out 70 degrees and just flip it over to the negative side of x? I'm greatly confused here ^^

[floodhound2]

Ok so I was solving a trigonometry problem, and it was going pretty well i thought, until I checked the answers in the back of the book.


The assignment is "Without a calculator define the angles in 0 <= v <= 180 (degrees) which is the solution for..."

This is translated to

180 - 70 = 110 so then cos110 = -.342

And, what does -cos70 mean then?

Good question ! Cant put it in words yet maybe cause its the csc? since cos is negative then the opposite is the csc = csc.342 = 70 ?

Perhaps I need a refresher and zooming in on the csc? the "inverse of cos"

Reminds me of a fraction that has a negative denominator, simply invert and make positive.

[bad_brain]

*brain exploded because when optimizing mysql I even needed a calculator to check how many Bytes 16MB is*

[ayu]

Good question ! Cant put it in words yet maybe cause its the csc? since cos is negative then the opposite is the csc = csc.342 = 70 ?

Perhaps I need a refresher and zooming in on the csc? the "inverse of cos"

Reminds me of a fraction that has a negative denominator, simply invert and make positive.

hmm, so csc342 = -cos70 ?

csc doesn't look like the negative of cos according tho this, seeing that it's vertical.

Code: Select all

http://upload.wikimedia.org/wikipedia/commons/9/9d/Circle-trig6.svg

[floodhound2]

well since the cos is adjacent / hypotenuse or

cos=A/B

then cant you say that

CSC=B/A

Thus if I have COS-70 =.342 then I could say that CSC.342 = 70

take a look at the tables listed in Basic relationships

http://en.wikipedia.org/wiki/Trigonometric_identities

It shows what i am trying to say

Oh btw.

hmm, so csc342 = -cos70 ?

is not true

CSC.342 = 70

Hell maybe i am way off don't know

[ayu]

well since the cos is adjacent / hypotenuse or

cos=A/B

then cant you say that

CSC=B/A

Thus if I have COS-70 =.342 then I could say that CSC.342 = 70

Well I get that cos-70 = .342 and arcsin.342 = 70...

apparently cos(70) = cos(-70) = .342

while -cos(70) = -.342

So yeah I get the result that the book wanted now. Basically I can take the result form cos70/-70 and invert it ^^


Thanks for your time Floodie

[floodhound2]

Well thanks to you.

Now I can see that I need to refresh my trig studies. Of all the math practices this is one of my weakest. Anyways I guess we helped each other

[ayu]

Ok I have a new problem ^^



Define "a" so that the area becomes 24 cm^2


Now, I know that a = (sin(150) * 24) - 4

a = 8


The problem is that I can't really prove the theory. As in I can't really tell how I got to that solution, it was simply a good guess I made when I ran out of options....


What I did to solve it in the first place was:

Area = a * (a + 4) * sin(150) / 2 = 24

a^2 + 4a * sin150 = 48

a^2 + 4a = 96

But since I got stuck there....

I also reverted it to a ( a + 4 ) = 96. But still nothing that really gave me any answers.


And doing a = 96 / (a + 4) doesn't really help either ^^

Does anyone know a solution?

[ayu]

Ok I solved it ^^


since a^2 + 4a = 96

then a^2 + 4a - 96 = 0

Now this is a "second degree equation" or how you say it in English. And by the looks of it, I can use the pq formula

Which goes that if x^2 + px + q

Then x = - p/2 (+-) √ (p/2)^2 - q

so... a = - 4/2 + √ (4/2)^2 - (-96) = -2 + 10 = 8

(or just 10 - 2)

So it makes perfect sense then that a = 8

[bad_brain]

gawd, this thread shows me how much I have forgotten since I've been in school...
but congrats for solving it...

[Swan]

and the only time I was more lost.... was when I saw a streetcar named desire and thought the lead actor was handsome

[Still_Learning]

I've never gotten past algerbra.. i changed my major study from computer science to liberal arts because they wanted me to take calculas classes and trig and all that, i HATE math..
its my absolute worst subject. - allthough i do see how important it is in programming unfortunately

[floodhound2]

I think that math is hated toward because of the lack of good instructors. I also hated math until I got a most impressive teacher, then it all changed.

Just keep in mind that the world is either math or religion.

[Swan]

“If in other sciences we should arrive at certainty without doubt and truth without error, it behooves us to place the foundations of knowledge in mathematics.”
- Roger Bacon

[ayu]

I think that math is hated toward because of the lack of good instructors. I also hated math until I got a most impressive teacher, then it all changed.

Just keep in mind that the world is either math or religion.

I totally agree! Before I went to uni, I really hated math because my teacher sucked at teaching it (she broadcasted on one frequency and I listened on another xD). She went through one thing the other day and told us that we would have a chance to do some assignments the next day for practice. But when we got there the next day it's like she just forgot what she said, and carried on to the next chapter, so if you weren't a very good listener at HER frequency, then you were fucked.

But now I have a perfect teacher who explains everything in detail which makes it a hell lot more fun!